Mark the incorrect statement for a particle going on a straight line.

Options

A. If the velocity and acceleration have opposite sign, then the object is slowing down.
B. IF the position and velocity have opposite sign, then the particle is moving towards the origin.
C. If the velocity is zero at an instant, then the acceleration should also be zero at that instant.
D. If the velocity is zero for a time interval, then the acceleration is zero at any instant within the time interval.

Answer

To solve the question, we need to analyze the statements provided and identify which one is incorrect regarding a particle moving in a straight line.

### Step-by-Step Solution:

1. **Understand the Statements**:
We have three statements to evaluate:
- Statement A: If the velocity and acceleration have opposite signs, then the object is slowing down.
- Statement B: If the position and velocity have opposite signs, then the particle is moving toward the origin.
- Statement C: If the velocity is zero at an instant, then the acceleration should also be zero at that instant.

2. **Evaluate Statement A**:
- If the velocity (v) is positive and the acceleration (a) is negative (or vice versa), the object will indeed slow down. This is correct as the acceleration is acting in the opposite direction to the velocity.
- **Conclusion**: Statement A is correct.

3. **Evaluate Statement B**:
- If the position is positive (to the right of the origin) and the velocity is negative (moving to the left), the particle is indeed moving toward the origin. This statement holds true.
- **Conclusion**: Statement B is correct.

4. **Evaluate Statement C**:
- If the velocity is zero at an instant, it does not imply that the acceleration must also be zero. A particle can have zero velocity while still experiencing acceleration (for example, at the peak of a projectile's motion).
- **Conclusion**: Statement C is incorrect.

5. **Final Answer**:
- The incorrect statement is **Statement C**: "If the velocity is zero at an instant, then the acceleration should also be zero at that instant."